Citation

Jamison S, McCartney M. Chaos 2007; 17(3): 033116.

Affiliation

School of Computing & Mathematics, University of Ulster, Newtownabbey BT37 0QB, Northern Ireland.

Copyright

(Copyright © 2007, American Institute of Physics)

DOI

10.1063/1.2752969

PMID

17902998

Abstract

Mathematical models that describe the dynamical behavior of a group of vehicles as they move along a stretch of road are known as car following models. They attempt to model the interactions between individual vehicles where the behavior of each vehicle is dependent on the motion of the vehicle directly in front and overtaking is not permitted. In this paper, the traditional car following model is modified by removing this "no overtaking" restriction and its behavior is investigated for a group of vehicles traveling on a closed loop. The resulting model is described in terms of a set of coupled time delay differential equations, and these are solved numerically to analyze their post transient behavior under a periodic perturbation. The effect of varying both the time taken for the driver to respond to the behavior of the vehicle in front and the length of the closed loop is examined. For certain parameter choices, the post transient behavior is found to be chaotic, and in these cases the degree of chaos is estimated using the Grassberger-Procaccia dimension.

Language: en